Logarithmic/linear scale formula for 0.2:5mil to 10:1mil

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I'm still trying to wrap my head around logs and figuring out how to derive formulas from given value pairs.

In this example, at a value of 0.2:5mil should be derived, and at 1:1mil (so it's an inverse scale?).

How can I find out the output for a given value, say 0.1?

Basically, the closer the value gets to zero, the higher the output should be.

I came across these two questions which are close to what I'm looking for but I'm still having trouble deriving these formulas.

Any help is very much appreciated.